I just googled and found more on the subject , it has been quite long time for me when I studied Material Science and technology . Here you can see Phonons are the culprit for the work being done for other materials .

http://en.wikipedia.org/wiki/Thermal_conductivity

"In metals, thermal conductivity approximately tracks electrical conductivity according to the Wiedemann-Franz law, as freely moving valence electrons transfer not only electric current but also heat energy. However, the general correlation between electrical and thermal conductance does not hold for other materials, due to the increased importance of phonon carriers for heat in non-metals. As shown in the table below, highly electrically conductive silver is less thermally conductive than diamond, which is a electrical insulator."

-AP